Integrated trophic position as a proxy for food-web complexity

There are two distinct approaches to describing the distributions of biomass and species in food webs: one to consider them as discrete trophic levels (TLs); and the other to consider them as continuous trophic positions (TPs). Bridging the gap between these two perspectives presents a nontrivial challenge in integrating biodiversity and food-web structure. Food network unfolding (FNU) is a technique used to bridge this gap by partitioning the biomass of species into integer TLs to compute three complexity indices, namely vertical (D-V), horizontal (D-H) and range (D-R) diversity (D indices), through decomposition of Shannon's index H '. Using FNU, the food web (a network of species with unique TPs) is converted to a linear food chain (a biomass distribution at discrete TLs). This enables us to expect that the unfolded biomass within species decreases exponentially as the TL increases. Under this condition, the mean TL value in unfolded food chains is hypothesized to have an exponential relationship with the vertical diversity, D-V. To explore this, we implemented FNU and calculated D indices for food webs publicly available at EcoBase (n = 158) and calculated the integrated TP (iTP), defined as the biomass-weighted average TP of a given food web. The iTP corresponds to the mean TL in unfolded food chains and can be empirically measured through compound-specific isotope analysis of amino acids (CSIA-AA). Although our analysis is biased towards marine ecosystems, we revealed an exponential relationship between iTP and D-V, suggesting that iTP can serve as a measurable proxy for D-V. Furthermore, we found a positive correlation between the iTP observed in the total communities (total iTP) and the iTPs of partial communities consisting only of species with 2.0 <= TP < 3.0 (partial iTP; r(2) = 0.48), suggesting that D-V can be predicted using partial iTP. Our findings suggest that the net effect of species diversity, excluding the effect of biomass (corresponding to H ' - D-V), on food-web complexity can be revealed by combining CSIA-AA with biodiversity analysis (e.g. environmental DNA).